Geodesic
Infinity Laplace equation with non-trivial right-hand side
Electronic journal of differential equations, Tome 2010 (2010)
We analyze the set of continuous viscosity solutions of the infinity Laplace equation $-\Delta^N_{\infty}w(x) = f(x)$, with generally sign-changing right-hand side in a bounded domain. The existence of a least and a greatest continuous viscosity solutions, up to the boundary, is proved through a Perron's construction by means of a strict comparison principle. These extremal solutions are proved to be absolutely extremal solutions.
Classification : 35J70, 35B35
Keywords: infinity Laplace equation, inhomogeneous equation, viscosity solutions, least solution, greatest solution, strict comparison principle, existence, uniqueness, local Lipschitz continuity 
@article{EJDE_2010__2010__a46,
     author = {Lu,  Guozhen and Wang,  Peiyong},
     title = {Infinity {Laplace} equation with non-trivial right-hand side},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1194.35194},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a46/}
}
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AU  - Wang,  Peiyong
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JO  - Electronic journal of differential equations
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%A Wang,  Peiyong
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%J Electronic journal of differential equations
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%V 2010
%U http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a46/
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Lu,  Guozhen; Wang,  Peiyong. Infinity Laplace equation with non-trivial right-hand side. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a46/